Introducing Students to Crosstabulation in Large Intro Courses

by: Tristan Bridges

This fall, we decided to continue a tradition in our department of stressing some basic statistical analysis in our lower-level courses. As a part of that, students in any section of Introduction to Sociology produce a data analysis project that has them rely on a small sample of variables from the General Social Survey to run and interpret a basic crosstabulation. This semester, I decided to try something new in my large lecture course: to teach students about crosstabulation, I had them produce a human crosstabulation using their bodies in the lecture hall (I wanted to do it out in the quad, but called it due to weather).

We started by separating the class into two groups: “traditional students” and “non-traditional students.” The College at Brockport has a large non-traditional student population. So, of the 112 students in my course (on the day of this exercise), I wasn’t surprised to learn that 41 of them classified themselves as “non-traditional.” For our purposes, we defined “traditional” students as 18-22 years old students who started college at The College at Brockport and live on campus.

Once in groups, I asked the students to think about their experience thus far at college. And everyone was asked to rank their satisfaction with their college experience so far as “less than satisfied,” “satisfied,” or “more than satisfied.” Although this is not a representative sample of Brockport students, we pretended that it was for the purposes of our analysis. And we discussed what that meant at the outset. I had students formulate a hypothesis about their perceptions of how student status (traditional or non) might affect how happy students are with their college experience. Everyone came to the same conclusion: the students thought that traditional students would be more likely to be satisfied. Once students had an idea about how satisfied (or not) they were with college, all of them arranged their bodies into a human frequency table. Then—of course—we all took selfies to commemorate the moment and tweeted them out (#drbridgeshumancrosstab).

The lion’s share of the students classified themselves as “satisfied” (93 of 112). 15 students were “less than satisfied” and only 4 students were “more than satisfied.” Of those 15 students who were “less than satisfied,” however, a larger number were non-traditional (9) than traditional (6) college students. We talked about these observed frequencies, discussing the fact that the numbers appeared to loosely confirm our hypothesis. While the raw numbers might look close, only 8.5% of traditional students were “less than satisfied” compared with 22% of non-traditional students. Certainly, it’s a difference. But, is the different large enough—again, pretending that this is a representative sample—to argue that student status is actually causing non-traditional students to have worse experiences? To answer that, we calculated Chi Square and tested our results for statistical significance.

Students in each of the cells first calculated what the expected frequencies would have been if student status had no impact on satisfaction with college. We compared these with our observed frequencies and I had students raise their hands if the expected frequency was higher or lower than the observed in the cell they occupied. Then, students in each cell used these two numbers to calculate the test statistic for their cell. We added all of these up to collectively produce a value for Chi Square for the class and compared it to a critical Chi table together.

I’m hoping that the human frequency table made learning something students sometimes struggle with more enjoyable. But, it also seemed like a fun way of reminding students that when they seem tables containing numbers sociologists use to make claims about people and the social world, those numbers are actually referring to people (just like us). So, we all performed a statistical analysis together (all 113 of us) before going online to look at how online modules can help do much of this for us.

If you’re interested, we did find a statistical relationship between student status and satisfaction with college. And we did not talk about alternative explanations for the finding. It’s not representative data, but it’s an interesting finding.

It’s a project I’m excited to continue in the course. Having better data literacy is something I’d like all of our students to achieve while at Brockport. Part of this involves understanding what the numbers and graphs mean. But, some of it involves an ability to look beyond the numbers and charts to see the people that comprise that data. Next time, I’ll make sure the weather cooperates.

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Thanks to Dr. Melody Boyd for enduring some of the exercise and helping me get some “action shots.”